The paradox of the early Bauhaus was that, although its manifesto proclaimed that the ultimate aim of all creative activity was building, the school did not offer classes in architecture until 1927.

The paradox was once discussed by St. Jerome in a sermon:

In early Islamic tradition liar paradox was discussed for at least 5 centuries starting from late 9th century apparently without being influenced by any other tradition.

Since initially ( B ) was not true and is now true, another paradox arises.

Since initially ( C ) was true and is now not true, it is a paradox.

The subject undoubtedly owed its sixteenth-century popularity to the paradox that it was considered more acceptable to depict a woman in the act of copulation with a swan than with a man.

In 1950, the idea was independently revived by Dutch astronomer Jan Hendrik Oort as a means to resolve a paradox: over the course of the Solar System's existence, the orbits of comets are unstable ; eventually, dynamics dictate that a comet must either collide with the Sun or a planet, or else be ejected from the Solar System by planetary perturbations.

According to Harrison, the first to conceive of anything like the paradox was Thomas Digges, who was also the first to expound the Copernican system in English and may have been the first to postulate an infinite universe with infinitely many stars.

The paradox is commonly attributed to the German amateur astronomer Heinrich Wilhelm Olbers, who described it in 1823, but Harrison shows convincingly that Olbers was far from the first to pose the problem, nor was his thinking about it particularly valuable.

Harrison argues that the first to set out a satisfactory resolution of the paradox was Lord Kelvin, in a little known 1901 paper, and that Edgar Allan Poe's essay Eureka ( 1848 ) curiously anticipated some qualitative aspects of Kelvin's argument:

However, the Big Bang theory introduces a new paradox: it states that the sky was much brighter in the past, especially at the end of the recombination era, when it first became transparent.

This would not resolve the paradox given the following argument: According to the laws of thermodynamics, the intermediate matter must eventually heat up ( or cool down, if it was initially hotter ) until it is in thermal equilibrium with the surrounding stars.

It even eludes the idea a lot more even to assume the concept of " nothing " or negation was created, therefore it is seemingly impossible to conceive such a notion where it draws down to a paradox.

Plato, as seen in the dialogue Parmenides, was willing to accept a certain amount of paradox with his forms.

Thus, it was important to uncover the hidden patterns of circularity, self-reference and paradox within a given set of statements rather that feign objectivity, as such an investigation might allow new perspectives to have influence and new practices to be sanctioned or adopted.

Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory.

The grandfather paradox, for example, would arise if a time traveler were to kill his own grandfather before his mother or father was conceived, thereby preventing his own birth.

Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays, if he was born on a leap day.

However, he was also the first to notice some of the apparently exotic consequences of entanglement, and used them to formulate the Einstein-Podolsky-Rosen paradox in the hope of showing that quantum mechanics had unacceptable implications.

The name " quine " was coined by Douglas Hofstadter, in his popular science book Gödel, Escher, Bach: An Eternal Golden Braid, in the honor of philosopher Willard Van Orman Quine ( 1908 – 2000 ), who made an extensive study of indirect self-reference, and in particular for the following paradox-producing expression, known as Quine's paradox:

Research into quantum entanglement was initiated by a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen describing the EPR paradox and several papers by Erwin Schrödinger shortly thereafter.

In this study, they formulated the EPR paradox ( Einstein, Podolsky, Rosen Paradox ), a thought experiment that attempted to show that quantum mechanical theory was incomplete.

Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry ( 1867 – 1928 ), a junior librarian at Oxford's Bodleian library, who had suggested the more limited paradox arising from the expression " the first undefinable ordinal ".

Eureka: A Prose Poem, an essay written in 1848, included a cosmological theory that presaged the Big Bang theory by 80 years, as well as the first plausible solution to Olbers ' paradox.

The first paradox ( the Liar ) is probably the most famous, and is similar to the famous paradox of Epimenides the Cretan.

The first aspect of the paradox, " the argument by scale ", is a function of the raw numbers involved: there are an estimated 200 – 400 billion ( 2 – 4 × 10 < sup > 11 </ sup >) stars in the Milky Way and 70 sextillion ( 7 × 10 < sup > 22 </ sup >) in the visible universe.

The second cornerstone of the Fermi paradox is a rejoinder to the argument by scale: given intelligent life's ability to overcome scarcity, and its tendency to colonize new habitats, it seems likely that at least some civilizations would be technologically advanced, seek out new resources in space and then colonize first their own star system and subsequently the surrounding star systems.

It is said that when Wittgenstein first heard this paradox one evening ( which Moore had earlier stated in a lecture ), he rushed round to Moore's lodgings, got him out of bed and insisted that Moore repeat the entire lecture to him.

Naṣīr al-Dīn al-Ṭūsī could have been the first logician to identify the liar paradox as self-referential.

The multi-sentence version of the liar paradox generalizes to any circular sequence of such statements ( wherein the last statement asserts the truth / falsity of the first statement ), provided there are an odd number of statements asserting the falsity of their successor ; the following is a three-sentence version, with each statement asserting the falsity of its successor:

Roughly speaking, in proving the first incompleteness theorem, Gödel used a slightly modified version of the liar paradox, replacing " this sentence is false " with " this sentence is not provable ", called the " Gödel sentence G ".

George Boolos has since sketched an alternative proof of the first incompleteness theorem that uses Berry's paradox rather than the liar paradox to construct a true but unprovable formula.

Classical measure theory makes deep usage of the axiom of choice, which is fundamental to, first, distinction between measurable and non-measurable sets, the existence of the latter being behind such famous results as the Banach – Tarski paradox, and secondly the hierarchies of notions of measure captured by notions such as Borel algebras, which are an important source of intuitions in set theory.

Peirce begins with the observation that " Berkeley's metaphysical theories have at first sight an air of paradox and levity very unbecoming to a bishop ".

Epicurus is generally credited with first expounding the problem of evil, and it is sometimes called " the Epicurean paradox " or " the riddle of Epicurus ":

Such puzzles as the Sorites paradox and the related continuum fallacy have raised doubt as to the applicability of classical logic and the principle of bivalence to concepts that may be vague in their application.

This theory solves the paradox of how it could be possible for antibodies to be raised against the intracellular antigenic targets of ANCA.

In philosophy and logic, the liar paradox or liar's paradox ( pseudomenon in Ancient Greek ) is the statement " this sentence is false.

One version of the liar paradox is attributed to the Greek philosopher Eubulides of Miletus who lived in the 4th century BC.

* In the novel Small Gods by Terry Pratchett the prophet Brutha encounters several Ephebian ( Greek ) philosophers in the country, attempting to disprove Zeno's paradox by shooting arrows at a succession of tortoises.

The paradox that Greek presence was more prominent in Bactria than in areas far closer to Greece can possibly be explained by past deportations of Greeks to Bactria.

For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy .< ref name =" Stillwell Infinite Series Early Results "> Later, Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids.

: Origin: < Middle French, French paradoxe ( 1495 as noun ; 1372 – 4 in plural paradoxesas the title of a work by Cicero ; paradoxon ( noun ) philosophical paradox in post-classical Latin also a figure of speech < ancient Greek παράδοξον, especially in plural παράδοξαStoical paradoxes, use as noun of neuter singular of παράδοξος ( adjective ) contrary to received opinion or expectation < παρα-para-prefix1 + δόξαopinion ( see doxology n .), after ancient Greek παρὰ δόξανcontrary to expectation.

The Greek philosopher Heraclitus attempted to solve the paradox by introducing the idea of a river where water replenishes it.

A dual example of a predestination paradox is depicted in the classic Ancient Greek play ' Oedipus ':

The paradox that Greek presence was more prominent in Bactria than in areas far closer to Greece can possibly be explained by the supposed policy of Persian kings to deport unreliable Greeks to this the most remote province of their huge empire.

Aristotle's wheel paradox is a paradox from the Greek work Mechanica traditionally attributed to Aristotle.